The Sobolev capacity on metric spaces

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The Sobolev capacity on metric spaces. / Kinnunen, Juha; Martio, Olli.

In: ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, Vol. 21, No. 2, 1996, p. 367-382.

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@article{02959777d780486c801b9d118d3411f3,
title = "The Sobolev capacity on metric spaces",
abstract = "We develop a capacity theory based on the definition of Sobolev functions on metric spaces with a Borel regular outer measure. Basic properties of capacity, including monotonicity, countable subadditivity and several convergence results, are studied. As an application we prove that each Sobolev function has a quasicontinuous representative. For doubling measures we provide sharp estimates for the capacity of balls. Capacity and Hausdorff measures are related under an additional regularity assumption on the measure.",
author = "Juha Kinnunen and Olli Martio",
year = "1996",
language = "English",
volume = "21",
pages = "367--382",
journal = "ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA",
issn = "1239-629X",
number = "2",

}

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TY - JOUR

T1 - The Sobolev capacity on metric spaces

AU - Kinnunen, Juha

AU - Martio, Olli

PY - 1996

Y1 - 1996

N2 - We develop a capacity theory based on the definition of Sobolev functions on metric spaces with a Borel regular outer measure. Basic properties of capacity, including monotonicity, countable subadditivity and several convergence results, are studied. As an application we prove that each Sobolev function has a quasicontinuous representative. For doubling measures we provide sharp estimates for the capacity of balls. Capacity and Hausdorff measures are related under an additional regularity assumption on the measure.

AB - We develop a capacity theory based on the definition of Sobolev functions on metric spaces with a Borel regular outer measure. Basic properties of capacity, including monotonicity, countable subadditivity and several convergence results, are studied. As an application we prove that each Sobolev function has a quasicontinuous representative. For doubling measures we provide sharp estimates for the capacity of balls. Capacity and Hausdorff measures are related under an additional regularity assumption on the measure.

UR - http://www.scopus.com/inward/record.url?scp=0000130594&partnerID=8YFLogxK

M3 - Article

VL - 21

SP - 367

EP - 382

JO - ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA

JF - ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA

SN - 1239-629X

IS - 2

ER -

ID: 5434789